2/3x-5-2x=-13

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Solution for 2/3x-5-2x=-13 equation:



2/3x-5-2x=-13
We move all terms to the left:
2/3x-5-2x-(-13)=0
Domain of the equation: 3x!=0
x!=0/3
x!=0
x∈R
We add all the numbers together, and all the variables
-2x+2/3x+8=0
We multiply all the terms by the denominator
-2x*3x+8*3x+2=0
Wy multiply elements
-6x^2+24x+2=0
a = -6; b = 24; c = +2;
Δ = b2-4ac
Δ = 242-4·(-6)·2
Δ = 624
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:
$\sqrt{\Delta}=\sqrt{624}=\sqrt{16*39}=\sqrt{16}*\sqrt{39}=4\sqrt{39}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-4\sqrt{39}}{2*-6}=\frac{-24-4\sqrt{39}}{-12} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+4\sqrt{39}}{2*-6}=\frac{-24+4\sqrt{39}}{-12} $

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